@InProceedings{Andrej2018,
  author =       {J. {Andrej} and T. {Meurer}},
  title =        {Flatness-based constrained optimal control of
                  reaction-diffusion systems},
  booktitle =    {2018 Annual American Control Conference (ACC)},
  year =         2018,
  pages =        {2539-2544},
  month =        {June},
  doi =          {10.23919/ACC.2018.8431201},
  issn =         {2378-5861},
}

@Misc{Angeloudis2017,
  author =       {Athanasios Angeloudis and Matthew D. Piggott and
                  Stephan C. Kramer and Alexandros Avdis and Daniel
                  Coles and Marios Christou},
  title =        {{Comparison of 0-D, 1-D and 2-D model capabilities
                  for tidal range energy resource assessments}},
  year =         2017,
  eprint =       {sjxf4},
  archiveprefix ={EarthArXiv},
  doi =          {10.17605/osf.io/sjxf4}
}

@Article{Angeloudis2018,
  author =       {Athanasios Angeloudis and Stephan C. Kramer and
                  Alexandros Avdis and Matthew D. Piggott},
  title =        {Optimising tidal range power plant operation},
  journal =      {Applied Energy},
  year =         2018,
  volume =       212,
  pages =        {680 - 690},
  issn =         {0306-2619},
  doi =          {10.1016/j.apenergy.2017.12.052},
}

@InProceedings{Angeloudis2018a,
  author =       {Angeloudis, A and Hawkins, N and Kramer, SC and
                  Piggott, MD},
  title =        {Comparison of twin-basin lagoon systems against
                  conventional tidal power plant designs},
  booktitle =    {Advances in Renewable Energies Offshore: Proceedings
                  of the 3rd International Conference on Renewable
                  Energies Offshore (RENEW 2018), October 8-10, 2018,
                  Lisbon, Portugal},
  year =         2018,
  pages =        159,
  organization = {CRC Press}
}

@Article{Angeloudis2019,
  author =       {Angeloudis, Athanasios},
  title =        {Tidal range structure operation assessment and
                  optimisation},
  journal =      {Dams and Reservoirs},
  year =         2019,
  volume =       29,
  number =       2,
  pages =        {45-54},
  doi =          {10.1680/jdare.18.00042},
}

@Misc{Barral2016,
  author =       {Barral, Nicolas and Knepley, Matthew G and Lange,
                  Michael and Piggott, Matthew D and Gorman, Gerard J},
  title =        {{Anisotropic mesh adaptation in Firedrake with PETSc
                  DMPlex}},
  year =         2016,
  primaryclass = {math.NA},
  eprint =       {1610.09874},
  archiveprefix ={arXiv},
  url =          {http://arxiv.org/abs/1610.09874},
}

@Misc{Bauer2018,
  author =       {Werner Bauer and Colin J. Cotter},
  title =        {{Energy-enstrophy conserving compatible finite
                  element schemes for the shallow water equations on
                  rotating domains with boundaries}},
  year =         2018,
  archiveprefix ={arXiv},
  eprint =       {1801.00691},
  primaryclass = {math.NA},
  url =          {https://arxiv.org/abs/1801.00691}
}

@Misc{Bendall2017,
  author =       {Bendall, Thomas M and Cotter, Colin J},
  title =        {{Statistical properties of an enstrophy conserving
                  discretisation for the stochastic quasi-geostrophic
                  equation}},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1710.04845},
  primaryclass = {math.NA}
}

@Misc{Bihlo2019,
  author =       {Alex Bihlo and James Jackaman and Francis
                  Valiquette},
  title =        {On the development of symmetry-preserving finite
                  element schemes for ordinary differential equations},
  year =         2019,
  eprint =       {1907.00961},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
}

@InProceedings{Bokhove2016,
  author =       {Onno Bokhove and Anna Kalogirou},
  title =        {Variational water wave modelling: from continuum to
                  experiment},
  booktitle =    {Lectures on the theory of water waves},
  year =         2016,
  editor =       {Thomas J. Bridges and Mark D. Groves and David P.
                  Nicholls},
  volume =       426,
  series =       {LMS Lecture Note Series},
  pages =        {226--260},
  publisher =    {Cambridge University Press},
  url =
                  {http://www1.maths.leeds.ac.uk/~matak/documents/lms-cup2015.pdf}
}

@Article{Braun2017,
  author =       {Moritz Braun and Kingsley O. Obodo},
  title =        {Multi-domain muffin tin finite element density
                  functional calculations for small molecules},
  journal =      {Computers & Mathematics with Applications},
  year =         2017,
  issn =         {0898-1221},
  doi =          {10.1016/j.camwa.2016.12.003},
  url =
                  {http://www.sciencedirect.com/science/article/pii/S0898122116306745},
}

@Article{Budd2018,
  author =       {Budd, Chris J. and McRae, Andrew T.T. and Cotter,
                  Colin J.},
  title =        {{The scaling and skewness of optimally transported
                  meshes on the sphere}},
  journal =      {Journal of Computational Physics},
  year =         2018,
  volume =       375,
  pages =        {540--564},
  doi =          {10.1016/j.jcp.2018.08.028},
  eprint =       {1711.00260},
  archiveprefix ={arXiv}
}

@Article{Chang2017,
  author =       {Chang, J. and Nakshatrala, K.B. and Knepley, M.G.
                  and Johnsson, L.},
  title =        {A performance spectrum for parallel computational
                  frameworks that solve PDEs},
  journal =      {Concurrency and Computation: Practice and
                  Experience},
  year =         2017,
  volume =       30,
  number =       11,
  pages =        {e4401},
  keywords =     {finite element methods, hardware architecture, high
                  performance computing, parallel computing,
                  scientific software, solvers and preconditioners},
  doi =          {10.1002/cpe.4401},
  url =
                  {https://onlinelibrary.wiley.com/doi/abs/10.1002/cpe.4401},
  eprint =       {1705.03625},
  archiveprefix ={arXiv},
}

@Article{Chang2017a,
  author =       {J. Chang and K.B. Nakshatrala},
  title =        {Variational inequality approach to enforcing the
                  non-negative constraint for advection–diffusion
                  equations},
  journal =      {Computer Methods in Applied Mechanics and
                  Engineering},
  year =         2017,
  volume =       320,
  pages =        {287-334},
  issn =         {0045-7825},
  eprint =       {1611.08758},
  archiveprefix ={arXiv},
  primaryclass = {cs.CE},
  doi =          {10.1016/j.cma.2017.03.022},
}

@PhdThesis{Chang2017b,
  author =       {Justin Chang},
  title =        {Structure-preserving high performance computational
                  methods for transport in porous media},
  school =       {University of Houston},
  year =         2017
}

@Misc{Chang2018,
  author =       {J. Chang and M. S. Fabian and M. G. Knepley and R.
                  T. Mills},
  title =        {{Comparative study of finite element methods using
                  the Time-Accuracy-Size (TAS) spectrum analysis}},
  year =         2018,
  archiveprefix ={arXiv},
  primaryclass = {cs.MS},
  eprint =       {1802.07832},
  url =          {https://arxiv.org/abs/1802.07832}
}

@Misc{Chiw2017,
  author =       {Charisee Chiw and Gordon Kindlmann and John Reppy},
  title =        {{An exploiration to visualize finite element data
                  with a DSL}},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1706.05718},
  primaryclass = {cs.HC}
}

@Article{Cotter2014,
  author =       {Colin J. Cotter and Robert C. Kirby},
  title =        {Mixed finite elements for global tide models},
  journal =      {Numerische Mathematik},
  year =         2015,
  pages =        {1--23},
  doi =          {10.1007/s00211-015-0748-z},
  url =          {http://arxiv.org/abs/1410.0045}
}

@Misc{Cotter2015,
  author =       {Colin J. Cotter and David A. Ham and Andrew T. T.
                  McRae and Lawrence Mitchell and Andrea Natale},
  title =        {On the shallow atmosphere approximation in finite
                  element dynamical cores},
  year =         2015,
  url =          {http://arxiv.org/abs/1410.3069},
  archiveprefix ={arXiv},
  eprint =       {1410.3069}
}

@Article{Cotter2016,
  author =       {Colin J. Cotter and Dmitri Kuzmin},
  title =        {Embedded discontinuous {Galerkin} transport schemes
                  with localised limiters},
  journal =      {Journal of Computational Physics},
  year =         2016,
  volume =       311,
  pages =        {363--373},
  archiveprefix ={arXiv},
  eprint =       {1509.04431},
  primaryclass = {math.NA},
  doi =          {10.1016/j.jcp.2016.02.021},
  url =          {http://arxiv.org/abs/1509.04431},
}

@Article{Cotter2018,
  author =       {Colin J. Cotter and P. Jameson Graber and Robert C.
                  Kirby},
  title =        {{Mixed finite elements for global tide models with
                  nonlinear damping}},
  journal =      {Numerische Mathematik},
  year =         2018,
  volume =       140,
  issue =        4,
  doi =          {10.1007/s00211-018-0980-4},
  archiveprefix ={arXiv},
  eprint =       {1706.01352},
  primaryclass = {math.NA}
}

@Article{Cotter2019,
  author =       {Cotter, Colin and Crisan, Dan and Holm, Darryl D and
                  Pan, Wei and Shevchenko, Igor},
  title =        {{Numerically Modeling Stochastic Lie Transport in
                  Fluid Dynamics}},
  journal =      {Multiscale Modeling \& Simulation},
  year =         2019,
  volume =       17,
  number =       1,
  pages =        {192--232},
  publisher =    {SIAM},
  doi =          {10.1137/18M1167929},
  archiveprefix ={arXiv},
  primaryclass = {physics.flu-dyn},
  eprint =       {1801.09729},
}

@Article{Eldred2019,
  author =       {Eldred, Christopher and Dubos, Thomas and Kritsikis,
                  Evaggelos},
  title =        {{A quasi-Hamiltonian discretization of the thermal
                  shallow water equations}},
  journal =      {Journal of Computational Physics},
  year =         2019,
  volume =       379,
  pages =        {1--31},
  publisher =    {Elsevier},
  archiveprefix ={HAL},
  doi =          {10.1016/j.jcp.2018.10.038},
  eprint =       {hal-01847698},
}

@Article{Farrell2019,
  author =       {Patrick E. Farrell and Lawrence Mitchell and Florian
                  Wechsung},
  title =        {{An augmented Lagrangian preconditioner for the 3D
                  stationary incompressible Navier–-Stokes equations
                  at high Reynolds number}},
  journal =      {SIAM Journal on Scientific Computing},
  volume =       41,
  pages =        {A3073-A3096},
  issue =        5,
  year =         2019,
  archiveprefix ={arXiv},
  eprint =       {1810.03315},
  primaryclass = {math.NA}
}

@Misc{Farrell2019a,
  author =       {Patrick E. Farrell and Pablo Alexei Gazca-Orozco and
                  Endre S\"uli},
  title =        {{Numerical Analysis of Unsteady Implicitly
                  Constituted Incompressible Fluids: Three-Field
                  Formulation}},
  year =         2019,
  eprint =       {1904.09136},
  archiveprefix ={arXiv},
  primaryclass = {math.NA}
}

@Misc{Farrell2019b,
  author =       {Patrick E. Farrell and Yunhui He and Scott P.
                  MacLachlan},
  title =        {{A local Fourier analysis of additive Vanka
                  relaxation for the Stokes equations}},
  year =         2019,
  eprint =       {1908.09949},
  archiveprefix ={arXiv},
  primaryclass = {math.NA}
}

@Article{Farrell2019c,
  author =       {Patrick E. Farrell and Matteo Croci and Thomas M.
                  Surowiec},
  title =        {Deflation for semismooth equations},
  journal =      {Optimization Methods and Software},
  year =         2019,
  volume =       0,
  number =       0,
  pages =        {1-24},
  publisher =    {Taylor & Francis},
  doi =          {10.1080/10556788.2019.1613655},
  archiveprefix ={arXiv},
  eprint =       {1904.13299},
  primaryclass = {math.OC}
}

@Book{Gibson2019,
  author =       {Thomas H. Gibson and Andrew T.T. McRae and Colin J.
                  Cotter and Lawrence Mitchell and David A. Ham},
  title =        {{Compatible Finite Element Methods for Geophysical
                  Flows: automation and implementation using Firedrake}},
  publisher =    {Springer International Publishing},
  year =         2019,
  doi =          {10.1007/978-3-030-23957-2},
  url =          {https://doi.org/10.1007/978-3-030-23957-2}
}

@Article{Gidel2017,
  author =       {Gidel, F. and Bokhove, O. and Kalogirou, A.},
  title =        {Variational modelling of extreme waves through
                  oblique interaction of solitary waves: application
                  to {Mach} reflection},
  journal =      {Nonlinear Processes in Geophysics},
  year =         2017,
  volume =       24,
  pages =        {43--60},
  doi =          {10.5194/npg-24-43-2017}
}

@InProceedings{Gidel2017a,
  author =       {Floriane Gidel and Onno Bokhove and Mark Kelmanson},
  title =        {Driven nonlinear potential flow with wave breaking
                  at shallow-water beaches},
  booktitle =    {Proceedings of the ASME 2017 36th International
                  Conference on Ocean, Offshore and Arctic
                  Engineering},
  year =         2017,
  pages =        {V001T01A053},
  doi =          {10.1115/omae2017-61974}
}

@Misc{Gjerde2018,
  author =       {Ingeborg G. Gjerde and Kundan Kumar and Jan M.
                  Nordbotten and Barbara Wohlmuth},
  title =        {Splitting method for elliptic equations with line
                  sources},
  year =         2018,
  archiveprefix ={arXiv},
  eprint =       {1810.12979},
  primaryclass = {math.NA}
}

@Article{Harcourt2019,
  author =       {Freddie Harcourt and Athanasios Angeloudis and
                  Matthew D. Piggott},
  title =        {Utilising the flexible generation potential of tidal
                  range power plants to optimise economic value},
  journal =      {Applied Energy},
  year =         2019,
  volume =       237,
  pages =        {873 - 884},
  issn =         {0306-2619},
  doi =          {10.1016/j.apenergy.2018.12.091},
  eprint =       {j2u9k},
  archiveprefix ={EarthArXiv},
}

@Misc{Iglesias2017,
  author =       {Jos\'e A. Iglesias and Kevin Sturm and Florian
                  Wechsung},
  title =        {Shape optimisation with nearly conformal
                  transformations},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1710.06496},
  primaryclass = {math.OC}
}

@Article{Iglesias2018,
  author =       {Iglesias, J. and Sturm, K. and Wechsung, F.},
  title =        {{Two-Dimensional Shape Optimization with Nearly
                  Conformal Transformations}},
  journal =      {SIAM Journal on Scientific Computing},
  year =         2018,
  volume =       40,
  number =       6,
  pages =        {A3807-A3830},
  doi =          {10.1137/17M1152711},
  eprint =       {1710.06496},
  archiveprefix ={arXiv},
  primaryclass = {math.OC},
}

@Misc{Jackaman2017,
  author =       {James Jackaman and Georgios Papamikos and Tristan
                  Pryor},
  title =        {{The design of conservative finite element
                  discretisations for the vectorial modified KdV
                  equation}},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1710.03527},
  primaryclass = {math.NA}
}

@Misc{Jackaman2018,
  author =       {James Jackaman and Tristan Pryor},
  title =        {{Conservative Galerkin methods for dispersive
                  Hamiltonian problems}},
  year =         2018,
  eprint =       {1811.09999},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
}

@Article{Jacobs2015,
  author =       {Christian T. Jacobs and Matthew D. Piggott},
  title =        {{Firedrake-Fluids} v0.1: numerical modelling of
                  shallow water flows using an automated solution
                  framework},
  journal =      {Geoscientific Model Development},
  year =         2015,
  volume =       8,
  number =       3,
  pages =        {533--547},
  url =          {http://www.geosci-model-dev.net/8/533/2015/},
  doi =          {10.5194/gmd-8-533-2015}
}

@Misc{Joshaghani2018,
  author =       {M. S. Joshaghani and S. H. S. Joodat and K. B.
                  Nakshatrala},
  title =        {A stabilized mixed discontinuous Galerkin
                  formulation for double porosity/permeability model},
  year =         2018,
  archiveprefix ={arXiv},
  eprint =       {1805.01389},
  primaryclass = {cs.CE}
}

@Article{Joshaghani2019,
  author =       {Joshaghani, MS and Chang, J and Nakshatrala, KB and
                  Knepley, Matthew G},
  title =        {Composable block solvers for the four-field double
                  porosity/permeability model},
  journal =      {Journal of Computational Physics},
  year =         2019,
  volume =       386,
  pages =        {428--466},
  publisher =    {Elsevier},
  doi =          {10.1016/j.jcp.2019.02.020},
  archiveprefix ={arXiv},
  eprint =       {1808.08328},
  primaryclass = {cs.CE},
}

@Article{Kalogirou2016,
  author =       {Anna Kalogirou and Erietta E. Moulopoulou and Onno
                  Bokhove},
  title =        {{Variational finite element methods for waves in a
                  Hele–Shaw tank}},
  journal =      {Applied Mathematical Modelling},
  year =         2016,
  pages =        {7493--7503},
  issn =         {0307-904X},
  doi =          {10.1016/j.apm.2016.02.036},
  url =
                  {http://www.sciencedirect.com/science/article/pii/S0307904X1630110X},
}

@InProceedings{Kalogirou2016a,
  author =       {Anna Kalogirou and Onno Bokhove},
  title =        {Mathematical and numerical modelling of wave impact
                  on wave-energy buoys},
  booktitle =    {Proceedings of the ASME 2016 35th International
                  Conference on Ocean, Offshore and Arctic
                  Engineering},
  year =         2016,
  pages =        {V007T06A067},
  doi =          {10.1115/OMAE2016-54937}
}

@InProceedings{Kalogirou2017,
  author =       {Anna Kalogirou and Onno Bokhove and David Ham},
  title =        {Modelling of Nonlinear Wave-Buoy Dynamics Using
                  Constrained Variational Methods},
  booktitle =    {Proceedings of the ASME 2017 36th International
                  Conference on Ocean, Offshore and Arctic
                  Engineering},
  year =         2017,
  pages =        {V07AT06A060},
  doi =          {10.1115/omae2017-61966}
}

@Article{Karna2018,
  author =       {K\"arn\"a, T. and Kramer, S. C. and Mitchell, L. and
                  Ham, D. A. and Piggott, M. D. and Baptista, A. M.},
  title =        {Thetis coastal ocean model: discontinuous Galerkin
                  discretization for the three-dimensional hydrostatic
                  equations},
  journal =      {Geoscientific Model Development},
  year =         2018,
  volume =       11,
  number =       11,
  pages =        {4359--4382},
  url =          {https://www.geosci-model-dev.net/11/4359/2018/},
  doi =          {10.5194/gmd-11-4359-2018}
}

@Misc{Kawecki2017,
  author =       {Ellya L. Kawecki},
  title =        {{A DGFEM for Uniformly Elliptic Two Dimensional
                  Oblique Boundary Value Problems}},
  year =         2017,
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  eprint =       {1711.01836}
}

@Article{Kawecki2019,
  author =       {Kawecki, Ellya L.},
  title =        {{A DGFEM for nondivergence form elliptic equations
                  with Cordes coefficients on curved domains}},
  journal =      {Numerical Methods for Partial Differential
                  Equations},
  year =         2019,
  volume =       35,
  number =       5,
  pages =        {1717-1744},
  doi =          {10.1002/num.22372},
  archiveprefix ={arXiv},
  eprint =       {1708.05028},
  primaryclass = {math.NA},
}

@Misc{Kawecki2019a,
  author =       {Ellya L. Kawecki},
  title =        {{Finite element theory on curved domains with
                  applications to DGFEMs}},
  year =         2019,
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  eprint =       {1903.08735}
}

@InProceedings{Lange2015,
  author =       {Lange, Michael and Knepley, Matthew G. and Gorman,
                  Gerard J.},
  title =        {{Flexible, Scalable Mesh and Data Management Using
                  PETSc DMPlex}},
  booktitle =    {Proceedings of the 3rd International Conference on
                  Exascale Applications and Software},
  year =         2015,
  series =       {EASC '15},
  pages =        {71--76},
  address =      {Edinburgh, Scotland, UK},
  publisher =    {University of Edinburgh},
  isbn =         {978-0-9926615-1-9},
  location =     {Edinburgh, UK},
  numpages =     6,
  url =          {http://dl.acm.org/citation.cfm?id=2820083.2820097},
  archiveprefix ={arXiv},
  primaryclass = {cs.MS},
  eprint =       {1505.04633}
}

@Misc{Mapakshi2017,
  author =       {N. K. Mapakshi and J. Chang and K. B. Nakshatrala},
  title =        {A scalable variational inequality approach for flow
                  through porous media models with pressure-dependent
                  viscosity},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1710.02620},
  primaryclass = {cs.ME}
}

@Article{McCormack2018,
  author =       {Kimberley A. McCormack and Marc A. Hesse},
  title =        {{Modeling the poroelastic response to megathrust
                  earthquakes: A look at the 2012 Mw 7.6 Costa Rican
                  event}},
  journal =      {Advances in Water Resources},
  year =         2018,
  volume =       114,
  pages =        {236-248},
  doi =          {10.1016/j.advwatres.2018.02.014}
}

@Article{McRae2018,
  author =       {Andrew T. T. McRae and Colin J. Cotter and Chris J.
                  Budd},
  title =        {{Optimal-Transport-Based Mesh Adaptivity on the
                  Plane and Sphere Using Finite Elements}},
  journal =      {SIAM Journal on Scientific Computing},
  year =         2018,
  volume =       40,
  number =       2,
  pages =        {A1121-A1148},
  doi =          {10.1137/16M1109515},
  eprint =       {1612.08077},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  url =          {http://arxiv.org/abs/1612.08077}
}

@Article{Natale2016,
  author =       {Andrea Natale and Jemma Shipton and Colin J. Cotter},
  title =        {Compatible finite element spaces for geophysical
                  fluid dynamics},
  journal =      {Dynamics and Statistics of the Climate System},
  year =         2016,
  volume =       1,
  issue =        1,
  doi =          {10.1093/climsys/dzw005},
  eprint =       {1605.00551},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  url =          {http://arxiv.org/abs/1605.00551}
}

@Article{Natale2016a,
  author =       {Andrea Natale and Colin J. Cotter},
  title =        {Scale-selective dissipation in energy-conserving
                  finite element schemes for two-dimensional
                  turbulence},
  journal =      {Quarterly Journal of the Royal Meteorological
                  Society},
  year =         2017,
  eprint =       {1611.02623},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  url =          {http://arxiv.org/abs/1611.02623},
  doi =          {10.1002/qj.3063},
}

@Article{Natale2017,
  author =       {Andrea Natale and Colin J. Cotter},
  title =        {{A variational $H(\mathrm{div})$ finite-element
                  discretization approach for perfect incompressible
                  fluids}},
  journal =      {IMA Journal of Numerical Analysis},
  year =         2017,
  pages =        {drx033},
  doi =          {10.1093/imanum/drx033}
}

@Article{Ovchinnikov2019,
  author =       {G. V. Ovchinnikov and D. Zorin and I. V. Oseledets},
  title =        {Robust regularization of topology optimization
                  problems with a posteriori error estimators},
  journal =      {Russian Journal of Numerical Analysis and
                  Mathematical Modelling},
  year =         2019,
  volume =       34,
  issue =        1,
  doi =          {10.1515/rnam-2019-0005},
  archiveprefix ={arXiv},
  eprint =       {1705.07316},
  primaryclass = {math.NA}
}

@Article{Paganini2018,
  author =       {Alberto Paganini and Florian Wechsung and Patrick E.
                  Farrell},
  title =        {{Higher-order moving mesh methods for
                  PDE-constrained shape optimization}},
  journal =      {SIAM Journal on Scientific Computing},
  year =         2018,
  volume =       40,
  number =       4,
  doi =          {10.1137/17M1133956},
  archiveprefix ={arXiv},
  eprint =       {1706.03117},
  primaryclass = {math.NA}
}

@Article{Pan2019,
  author =       {Wei Pan and Stephan C. Kramer and Matthew D.
                  Piggott},
  title =        {{Multi-layer non-hydrostatic free surface modelling
                  using the discontinuous Galerkin method}},
  journal =      {Ocean Modelling},
  year =         2019,
  volume =       134,
  pages =        {68-83},
  issn =         {1463-5003},
  doi =          {10.1016/j.ocemod.2019.01.003},
}

@Article{Pimanov2018,
  author =       {V. Pimanov and I. Oseledets},
  title =        {{Robust topology optimization using a posteriori
                  error estimator for the finite element method}},
  journal =      {Structural and Multidisciplinary Optimization},
  year =         2018,
  volume =       58,
  issue =        4,
  doi =          {10.1007/s00158-018-1985-4},
  archiveprefix ={arXiv},
  eprint =       {1712.03017},
  primaryclass = {math.NA},
  url =          {https://arxiv.org/abs/1712.03017}
}

@Article{Roy2019,
  author =       {Thomas Roy and Tom B. Jönsthövel and Christopher
                  Lemon and Andrew J. Wathen},
  title =        {A block preconditioner for non-isothermal flow in
                  porous media},
  journal =      {Journal of Computational Physics},
  year =         2019,
  volume =       395,
  pages =        {636-652},
  issn =         {0021-9991},
  doi =          {10.1016/j.jcp.2019.06.038},
  eprint =       {1902.00095},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
}

@Misc{Roy2019a,
  author =       {Thomas Roy and Tom B Jönsthövel and Christopher
                  Lemon and Andrew J Wathen},
  title =        {{A constrained pressure-temperature residual (CPTR)
                  method for non-isothermal multiphase flow in porous
                  media}},
  year =         2019,
  eprint =       {1907.04229},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
}

@InProceedings{Salwa2016,
  author =       {Salwa, Tomasz and Bokhove, Onno and Kelmanson, Mark
                  A.},
  title =        {{Variational modelling of wave-structure
                  interactions for offshore wind turbines}},
  booktitle =    {Proceedings of the 35th International Conference on
                  Offshore Mechanics and Arctic Engineering},
  year =         2016,
  volume =       {Volume 6: Ocean Space Utilization; Ocean Renewable
                  Energy},
  month =        {June},
  doi =          {10.1115/OMAE2016-54897}
}

@Article{Salwa2017,
  author =       {Salwa, Tomasz and Bokhove, Onno and Kelmanson, Mark
                  A.},
  title =        {{Variational modelling of wave--structure
                  interactions with an offshore wind-turbine mast}},
  journal =      {Journal of Engineering Mathematics},
  year =         2017,
  month =        {Sep},
  day =          15,
  issn =         {1573-2703},
  doi =          {10.1007/s10665-017-9936-4}
}

@Book{Schwedes2017,
  author =       {Tobias Schwedes and David A. Ham and Simon W. Funke
                  and Matthew D. Piggott},
  title =        {Mesh Dependence in {PDE}-Constrained Optimisation},
  publisher =    {Springer International Publishing},
  year =         2017,
  doi =          {10.1007/978-3-319-59483-5},
  url =          {https://doi.org/10.1007/978-3-319-59483-5}
}

@Misc{Shipton2017,
  author =       {Shipton, J. and Cotter, C. J.},
  title =        {{Higher-order compatible finite element schemes for
                  the nonlinear rotating shallow water equations on
                  the sphere}},
  year =         2017,
  archiveprefix ={arXiv},
  eprint =       {1707.00855},
  primaryclass = {math.NA},
}

@Article{Siebelts2018,
  author =       {Dirk Siebelts and Andreas Kater and Thomas Meurer},
  title =        {{Modeling and Motion Planning for an Artificial
                  Fishtail}},
  journal =      {IFAC-PapersOnLine},
  year =         2018,
  volume =       51,
  number =       2,
  pages =        {319--324},
  note =         {9th Vienna International Conference on Mathematical
                  Modelling},
  issn =         {2405-8963},
  doi =          {10.1016/j.ifacol.2018.03.055},
}

@Article{Vouriot2019,
  author =       {Vouriot, Carolanne VM and Angeloudis, Athanasios and
                  Kramer, Stephan C and Piggott, Matthew D},
  title =        {Fate of large-scale vortices in idealized tidal
                  lagoons},
  journal =      {Environmental Fluid Mechanics},
  year =         2019,
  volume =       19,
  number =       2,
  pages =        {329--348},
  publisher =    {Springer}
}

@Misc{Wimmer2019,
  author =       {Golo Wimmer and Colin Cotter and Werner Bauer},
  title =        {Energy conserving upwinded compatible finite element
                  schemes for the rotating shallow water equations},
  year =         2019,
  archiveprefix ={arXiv},
  eprint =       {1901.06349},
  primaryclass = {math.NA},
}

@Article{Yamazaki2017,
  author =       {Yamazaki, Hiroe and Shipton, Jemma and Cullen,
                  Michael J. P. and Mitchell, Lawrence and Cotter,
                  Colin J.},
  title =        {{Vertical slice modelling of nonlinear Eady waves
                  using a compatible finite element method}},
  journal =      {Journal of Computational Physics},
  year =         2017,
  volume =       343,
  pages =        {130--149},
  doi =          {10.1016/j.jcp.2017.04.006},
  eprint =       {1611.04929},
  archiveprefix ={arXiv},
  primaryclass = {math.NA},
  url =          {http://arxiv.org/abs/1611.04929}
}

@InProceedings{Wallwork2020,
  author =       {Joseph G Wallwork and Nicolas Barral and
                  David A Ham and Matthew D Piggott},
  title =        {{Anisotropic Goal-Oriented Mesh Adaptation in
                   Firedrake}},
  booktitle =    {Proceedings of the 28th International
                  Meshing Roundtable},
  year =         2020,
  pages =        {83--100},
  publisher =    {Zenodo},
  month =        feb,
  doi =          {10.5281/zenodo.3653373},
  url =          {https://doi.org/10.5281/zenodo.3653373}
}
